Sökning: "Lie-Poisson structure"

Hittade 3 avhandlingar innehållade orden Lie-Poisson structure.

  1. 1. Geometric discretization for incompressible magnetohydrodynamics on the sphere

    Författare :Michael Roop; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Lie-Poisson structure; magnetohydrodynamics; Hamiltonian dynamics; magnetic extension; Casimirs; symplectic Runge-Kutta integrators;

    Sammanfattning : Many physical processes are modelled by partial differential equations (PDE), and their efficient discretization is still a challenging problem and an actively developing field. An important class of models arising in mathematical physics represents PDEs formulated in terms of a Lie-Poisson structure on the dual of infinite-dimensional Lie algebras, such as the Lie algebra of vector fields. LÄS MER

  3. 2. Symplectic methods for isospectral flows and 2D ideal hydrodynamics

    Författare :Milo Viviani; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; Symplectic methods; Fluid dynamics; Integrability theory; Euler equations; Lie--Possion systems; Isospectral flows; Geometric integration; Structure preserving algorithms; Hamiltonian systems;

    Sammanfattning : The numerical solution of non-canonical Hamiltonian systems is an active and still growing field of research. At the present time, the biggest challenges concern the realization of structure preserving algorithms for differential equations on infinite dimensional manifolds. LÄS MER

  4. 3. Geometric Discretization in Shape analysis

    Författare :Erik Jansson; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; compressible fluids; diffeomorphisms; residual neural networks; quantization; machine learning; Shape analysis;

    Sammanfattning : Discretizations in shape analysis is the main theme of this licentiate thesis, which comprises two papers.  The first paper considers  the problem of finding a parameterized time-dependent vector field that warps an initial set of points to a target set of points. LÄS MER